univar_order

Univariate variable reordering, described in Genz and Bretz (2009)
If failed due to PD singularity, the unfinished order will be returned 
and a warning will be issued

Under a different representation of the multivariate normal (MVN) probability, we can use the Vecchia approximation to sample the integrand at a linear complexity with respect to n. Additionally, both the SOV algorithm from Genz (92) and the exponential-tilting method from Botev (2017) can be adapted to linear complexity. The reference for the method implemented in this package is Jian Cao and Matthias Katzfuss (2024) "Linear-Cost Vecchia Approximation of Multivariate Normal Probabilities" <doi:10.48550/arXiv.2311.09426>. Two major references for the development of our method are Alan Genz (1992) "Numerical Computation of Multivariate Normal Probabilities" <doi:10.1080/10618600.1992.10477010> and Z. I. Botev (2017) "The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting" <doi:10.48550/arXiv.1603.04166>.

Jian Cao 

VeccTMVN

Multivariate Normal Probabilities using Vecchia Approximation

Matthias Katzfuss 

univar_order function

<dl><dt>a</dt>
<dd>lower integration limits</dd>
<dt>b</dt>
<dd>upper integration limits</dd>
<dt>sigma</dt>
<dd>covariance matrix</dd></dl>

Arguments

Univariate variable reordering, described in Genz and Bretz (2009)
If failed due to PD singularity, the unfinished order will be returned 
and a warning will be issued — univar_order

<dl>

<dt>a</dt>
<dd>lower integration limits</dd>


<dt>b</dt>
<dd>upper integration limits</dd>


<dt>sigma</dt>
<dd>covariance matrix</dd>

</dl>

Univariate variable reordering, described in Genz and Bretz (2009)
If failed due to PD singularity, the unfinished order will be returned 
and a warning will be issued

univar_order: Univariate variable reordering, described in Genz and Bretz (2009) If failed due to PD singularity, the unfinished order will be returned and a warning will be issued

Description

Usage

Value

Arguments